Question

If y=9 when x=9, how do you find y when y=-27 given y varies inversely as x?

Answer 1

`x = -3` when `y = -27`

Explanation:

Inversely: `y = k/x " or using proportions: " y_1/y_2 = x_2/x_1`

Using the two step method , find `k` given `y " and " x`:

`9 = k/9`

Multiply both sides by `9` to eliminate the denominator on the right:

`9 * 9 = k/9 * 9/1`

`81 = k`

Now fill in the equation using `k`:

`(-27)/1 = 81/x`

Find `x` by using the cross product: `-27x = 81`

Divide both sides by `-27: " "(-27x)/-27 = 81/-27`

`x = -3`

Using Proportions: `y_1/y_2 = x_2/x_1`

`9/-27 = x/9`

Use the cross product: `-27 x = 81`

Divide both sides by `-27: " " (-27x)/-27 = 81/-27`

`x = -3`